When a poll reveals that, say, 20 percent of voters have a favorable impression of Candidate A, and 30 percent have an unfavorable impression, and 50 percent don't know enough to have any impression -- well, it's not great news, but it also says Candidate A has room to grow. He or she can work on that big group of undecideds and try to leave them with a favorable impression.

Clinton, perhaps the most famous woman in the United States, if not the world, doesn't have that opportunity. In the latest CNN poll of the Democratic presidential race, for example, just 3 percent said they have no opinion of her. Fifty percent said they have an unfavorable opinion her, versus 46 percent favorable.

For Clinton to surpass 50 percent favorable, she will have to convince people who already know her, and who have probably known her for years, to change their opinion of her. Not an easy task.

The CNN survey, and other similar polls released recently, shows some pretty significant structural problems for Clinton. One is the yawning divide between the opinions that men and women have of her.

"Want to talk gender gaps? She has a huge one," notes one adviser to a Republican presidential campaign. The adviser points to several in the CNN poll:

When asked whether Clinton "cares about people like you," 57 percent of women said yes, while just 36 percent of men said the same -- a 21-point gender gap.

When asked whether Clinton "inspires confidence," 57 percent of women said yes, while just 41 percent of men said so -- a 16-point gender gap.

When asked whether Clinton "is honest and trustworthy," 49 percent of women said yes, while just 34 percent of men agreed -- a 15-point gender gap.

When asked if they have an overall favorable or unfavorable opinion of Clinton, 54 percent of women said favorable, while just 38 percent of men said the same -- a 16-point gender gap.

"Those are the definition of problematic data," notes the GOP campaign adviser. "Imagine the story if these numbers existed for a Republican."

The numbers also suggest Clinton could have problems trying to match Barack Obama's winning performance in 2008 and 2012. Obama did well with women, winning 56 percent in 2008 and 55 percent in 2012, according to exit polls. Clinton might well replicate, or maybe even exceed, those numbers.

But Obama also did reasonably well with men, too -- winning 49 percent in 2008 and 45 percent in 2012. Can Clinton do that? It's unclear.

It should be noted that simply having an unfavorable impression of a candidate does not mean a voter will not vote for that candidate; faced with an either-or choice in a general election, voters often hold their noses and cast a ballot for a candidate they don't really like. But the more voters dislike Clinton, the greater Republicans' chances of winning undecided voters.

GOP candidates increasingly see openings to press Clinton on the three topics dogging her campaign today -- her secret email system, the Clinton Foundation's financial affairs, and Benghazi -- as well as Clinton's near-total silence on all of them.

"The press avoidance and scandals are starting to take a toll," says an adviser for another GOP campaign. "Her numbers are sliding backwards as the curtain is starting to get drawn on a lot of these issues. There are definitely opportunities for Republicans."

There are signs some Republicans are already benefiting. In CNN's poll back in March, Clinton led Marco Rubio in a head-to-head matchup 55 percent to 42 percent. In the new poll, she leads Rubio 49 percent to 46 percent.

Of course the GOP has problems of its own, but numbers like that convince Republicans they are on the right track -- and that Clinton herself will continue to help them in the polls.

"With every shoe that drops, people become more and more convinced that Hillary Clinton cannot be trusted," says an aide at yet another GOP campaign. "They increasingly believe she's in this for herself, and that entrusting her with our safety and security is a really, really bad idea."